Line 2 baking sheets with silpats, and set aside. Chop chocolate into 1/4-inch chunks; set aside. In a medium bowl, sift together flour, baking soda, ground ginger, cloves, nutmeg, and cocoa. In the bowl of an electric mixer fitted with the paddle attachment, cream grated ginger and butter until light and fluffy, about 4 minutes. Add brown sugar; beat until combined. Add molasses; beat until combined. Add the flour mixture in batches until fully incorporated. Mix in chocolate, cover with plastic wrap; refrigerate until firm, 2 hours or more.
Heat oven to 325 degrees F. Place the sugar in a pie plate. Using a 1-ounce ice-cream scoop, scoop the dough into a bowl filled with sugar. Roll each ball of dough in sugar. Bake until surface cracks slightly, 13 to 15 minutes. Let cool for 5 minutes, then transfer to a wire rack to cool completely.
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